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Siberian Advances in Mathematics

, Volume 25, Issue 1, pp 56–75 | Cite as

Asymptotics of mean value points in the Schwarz theorem for divided differences

  • Yu. G. Nikonorov
Article
  • 36 Downloads

Abstract

We establish inequalities describing the asymptotic behavior of mean value points in the sense of the Schwarz theoremfor general divided differences constructed for a function with a certain growth order at a given point. These inequalities generalize a number of known results, in particular, of ones connected with the asymptotics of Lagrange points in the Taylor formula.

Keywords

divided difference Schwarz theorem mean value theorem B-spline Peano kernel asymptotics of mean value points 

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Copyright information

© Allerton Press, Inc. 2015

Authors and Affiliations

  1. 1.Southern Mathematical Institute of VSC RAS and the Government of the Republic of North Ossetia — AlaniaVladikavkazRussia

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